Question

What is the equation of the line that is parallel to the line 5x 2y = 12 and passes through the point (−2, 4)? y = – five-halvesx – 1 y = – five-halvesx 5 y = two-fifthsx – 1 y = two-fifthsx 5

Answer 1

The answer is

`y = - (5)/(2) x - 1`

Explanation:

If two equations are parallel it means that both their gradients are equal. We were given the equation:

`5x + 2y = 12`

in order to find the gradient of this equation that we are given we have to ensure that it is in its simplest form:

`5x + 2y = 12 \\ 2y = 12 - 5x \\ (2y)/(2) = (12)/(2) - (5)/(2) x \\ y = 6 - (5)/(2) x \: \\ or \: \\ y = - (5)/(2) x + 6`

Therefore the gradient of the parallel line with points (-2, 4) is also -5/2

`y = mx + c \\ 4 = - ( 5)/(2) ( - 2) + c \\ 4 = (10)/(2) + c \\ 4 = 5 + c \\ 4 - 5 = c \\`

`c = - 1 \\ hence \: the \: equation \: for \: the \: \\ parallel \: line \: is \\ \: y = - (5)/(2) x - 1`